Is it considered safe-enough to only have a front-brake on a fixie in a urban area that has many hills? I've been considering buying one, but I want to get some opinions before I move forward.
Yes. The front brake provides basically all of the stopping power in a bicycle, and recent tests in Bicycle Quarterly show that, in emergency stops, the distraction of attempting to use the rear brake may even increase stopping distance. Maximum bicycle braking power is achieved just before the bicycle starts to pitch over, as the rear wheel lifts off the ground. Once that occurs, it's trivial to lock the rear wheel with a brake or by using your legs on a fixed gear.
The main disadvantage of having a front brake only in extremely hilly situations is not being able to dissipate some of the thermal load of braking between both rims, so you risk overheating the front.
There are situations, such as ice, or slick leafs covering the road surface that make application of the front brake dangerous. Generally the front brake does all of the stopping because it does not lose traction until the bike flips; however, in the aforementioned scenarios, the front wheel is likely to lose traction, pitching the bike and rider to the ground. In those cases, it is safer to slow down on the rear wheel, where a skid does not cause a total loss of control. Sheldon Brown definitely mentions this in the single speed section, where he recommends using both front and rear brakes on freewheeling bikes.
The rule about two brakes is a rule about redundancy: If one brake fails, the other can be used to safely slow you to a stop.
That said, a fixie already has some kind of a rear-brake built in: The fixed pedal connection. As long as you have your feet on your pedals, you can apply reverse force.
The only problematic thing about this pedal-rear-brake is, that it only works as long as your feet are actually on the pedals. And that is where the hills come in: Are you certain that you can keep your feet on your pedals, independent of the hill you are riding down? If so, I see no problem with front-brake only fixie. However, if you have a hill that requires you to apply some force from a normal brake to keep your speed controllable, you should have two independent normal brakes. Likewise, if you want the ability to let go of your pedals to go down a hill fast, you need a second normal brake. A fixie's gear is generally not suitable for riding down hills fast. So, either you limit your speed to what you can safely follow with your feet, or you use a second brake. I would definitely opt for the later.
As a youngster 55 years ago I understand the legal requirement was a front brake only on a fixed wheel bike and that was all many of us had. Living on the edge of the Fens in Peterborough we had access to miles of dead flat countryside and many riders used a 12 tooth rear sprocket for a really high gear. Hard to spin up initially but great for constant high speed on the flat. We also amused ourselves using lorries exiting Kates Cafe on the A1 to act as a windbreak riding inches behind them for perhaps 10 miles at a stint, risky but fun demanding sharp reflexes!
This is pretty subjective. I'd say it's preference. Some riders truly have enough skill on a fixed gear bike to go without a rear brake. Most do it because of convention. It's considered unfashionable to have a rear brake on a fixie, and for many fixed gear riders form trumps function. In my opinion its a little foolish not to have a rear brake. Backpedaling to stop on a fixie is bad for your knees and in an emergency stopping situation it's harder to give the bike the body english it may need while you're trying to push backwards on the pedals at the same time. On the flip side, having a rear brake on the bike isn't going to hurt anything, though some hipster might dock you on style points. In my book that's just another plus.
People saying that a rear brake is useless must not ride much. Fast, steep, technical descents are much faster with rear brake, as is tight urban commuting.. even on dry pavement.
I'd challenge anyone with no rear brake(fixed doesn't count) to a race anyday thru the city. I really couldn't see someone even staying with me for more than a few blocks. First couple 90deg turns at speed you will see how no rear brake performs.
Then throw some gravel or oily water into mix.. not even close.
To be clear, I DO consider a fixed wheel as being a good rear brake, I'm talking about no rear at all as some people seem to think would be adequate.
I say this is nonsense... The ability to have the back brake engaged until you flip is what you want in those situations where you are going to die. And in fact when you are in a situation when you are flipping and have to let go(RELEASE) of the front brake you want the rear brake to engaged when your rear tire touches again for that split second when your front is not engaged. Anyway, 10-20 percent braking is more than 0-percent rear braking when you are going to crash.
Sorry, I am old school and have road both coast as well as a zillion miles of intense city riding before there were any helmets and the only thing that ever saved me was my two brakes, not one... And I guess until you actually crash or experienced flipping thru the air you will never know how important your rear brake is..